Adaptation has the attributes of a private good that aims to protect a country from climate change, while mitigation, which contributes to the reduction of worldwide greenhouse gas emissions, has the properties of a public good. This paper attempts to investigate how the innovation of adaptation technology by a developed country (the North) may affect a developing country (the South) as well as the North through changes of mitigation in both countries. We show that the efficacy of adaptation determines the level of both countries' mitigation, and thereby causes them to be better or worse off. For both countries to be better off, it is required that the innovation be neither very effective nor very ineffective. Furthermore, we demonstrate that by introducing an international transfer system in which the North is taxed according to the level of adaptation, both countries can be better off even if the innovation is highly effective.